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On the Ranges of Certain Fractional Integrals

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto, Toronto, Ontario
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Suppose 1 ≦ P < ∞, μ is real, and denote by Lμ,p the collection of functions f, measurable on (0, ∞ ), and which satisfy

1.1

Also denote by [X] the collection of bounded operators from a Banach space X to itself. For v > 0, Re α > 0, Re β > 0, let

1.2

and

1.3

where ξ and η are complex numbers. Iv,α,ξ and Jv,β,η, are generalizations of the Riemann-Liouville and Weyl fractional integrals respectively, and consequently we shall refer to them as fractional integrals.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1198 - 1216
Copyright
Copyright © Canadian Mathematical Society 1972

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